Stats Day 16
More on Z-Scores and the Normal
Model (Using the Chart)
Do Now
•
On Desk: Z-score and 69-95-99.7 Rule
Worksheet
Example 1(on 68-95-99.7)
The SAT test as 3 parts:
Writing, Mth, and Critical
Reading. Each part has a
distribution that is roughly
unimodal and symmetric,
an overall mean of 500
and a standard deviation
of 100 for all test takers.
•
Suppose you earned a 600 on one part of the
SAT. Where do you stand among all students
who took the test?
1. Find Z score (600-500)/100 = 1
2. What percent is to the LEFT??
68% + ½(32%)= 84%
84th PERCENTILE
3. Do the same for a score of 700
Percentiles
•
What percentile are the following?
Find the percentile
N(35, 5)
84th percentile:
97.5th percentile:
50th percentile:
Example 2
(not on 68-95-99.7)
What if it is not EXACTLY 0, ±1, ±2, or
±3 standard deviations away from
mean?
• (what if z-score≠0, ±1, ±2, or ±3)
•
Suppose you earned a 680 on one part of the
SAT. Where do you stand among all students
who took the test? [N(500, 100)]
1. Find Z score (680-500)/100 = 1.8
1. What percent is to the LEFT??
WE HAVE A CHART FOR THAT
Z-SCORE CHART
Find your z-score
2. Draw a picture
3. Look up z-score to tell you percent to
the LEFT of your score (less than your
score) Note: this is the percentile
4. Determine if you want that percent
(less than given score) or
100-[that percent] - more than given
1.
Second side of
Practice Sheet
Z-Score
•
What is the likelihood that you
scored above a 20 on this last ACT
given N(18.8, 3.7)
Finding percents
between z-scores
•
What if I want to know the likelihood
that I will score between a 17 and a
24 on the ACT based on the ACT
distribution for the Pritzker senior
class: N(18.8, 3.7)
Find the following
1)
• 2)
• 3)
• 4)
• 5)
•
1.4 < z < 2.88
z<-0.11
z > 0.24
-1.31 < z < 2.1
0.12 < z < 1.43
Homework
•
Chapter 6: #29, 30, 33, 34, 37